Long had been allowed leave the Ireland camp on Monday in order to sort out his future after West Brom accepted a £5 million bid from Hull City for the striker.
However, the 26-year-old returned to training on Tuesday still under contract with the Baggies after the move collapsed, but Tardelli is adamant Long will not be fazed by the developments.
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James McCarthy was also given permission to join up late with the squad, sealing a £13 million transfer to Everton, and Tardelli believes the move will help the 22-year-old advance his career.
"It will decide whether he will progress or not as a player, and I think James has the possibility to become a very good player," Tardelli claimed.
Aidan McGeady is the most notable absentee for Friday's World Cup qualifier at the Aviva Stadium, but Tardelli said that his injury would not force the Irish management into any tactical changes.
"We play in the same style but McGeady is a good player for us and we are unhappy he is missing for us," said the former Juventus midfielder.
Tuesday's training session passed off without any fresh injury concerns, Marc Wilson was the only notable absentee due to an on-going ankle injury, while goalkeeping duo Darren Randolph and Millwall’s David Forde were having a separate gym session.